# Current Trends for State-of-Charge (SoC) Estimation in Lithium-Ion Battery Electric Vehicles

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## Abstract

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## 1. Introduction

## 2. Overview of BEV LIB SoC Modelling Approaches

#### 2.1. Physical Electrochemical Models

#### 2.2. Electrical Equivalent Circuit Models

#### 2.2.1. Integral-Order Models

_{int}model is the most used integral-order model [22]. The R

_{int}model structure is straightforward; however, it does not consider the polarization and diffusion dynamics. Liaw et al. [23] introduced the resistor–capacitor model, which is a first-order model capable of mimicking LIB charging and discharging behavior using one resistor–capacitor network. Additionally, the open-circuit voltage hysteresis behavior can be considered to improve model accuracy [24].

#### 2.2.2. Fractional-Order Models

#### 2.3. Data-Driven Models

## 3. State Estimation in BEV LIBs

#### 3.1. SoC in LIBs

#### 3.1.1. Coulomb Counting

#### 3.1.2. Open Circuit Voltage

#### 3.1.3. State of Health

#### 3.2. Estimation of Energy and Remaining Capacity

#### 3.2.1. Look-Up Tables

#### Open-Circuit Voltage

#### Impedance

#### 3.2.2. Ampere-Hour Integral

#### 3.2.3. Filter-Based

#### Linear Kalman Filter

#### Extended Kalman Filter

#### Adaptive Extended Kalman Filter

#### Sigma-Point Kalman Filter

#### Unscented Kalman Filter

#### Adaptive Unscented Kalman Filter

#### Central Difference Kalman Filter

#### Cubature Difference Kalman Filter

#### Particle Filter

#### Unscented Particle Filter

#### Cubature Particle Filter

#### 3.2.4. Observer-Based

#### Luenberger

#### Sliding Mode

#### Proportional Integral

#### H-Infinity

#### 3.2.5. Data-Driven

#### Genetic Algorithm

#### Support Vector Machines

#### Artificial Neural Networks

#### 3.3. Comparison of Approaches

#### 3.4. Errors in Modeling

#### 3.4.1. Capacity Induced Errors

#### 3.4.2. Initial SoC Error

#### 3.4.3. Current Measurement Error

#### 3.4.4. Model Prediction Error

#### 3.4.5. Voltage Measurement Error

## 4. Challenges in SoC Estimation in LiBs

#### 4.1. Advanced Optical Fiber Sensing

#### 4.2. Multi-State Estimation

#### 4.3. Battery Model Selection and Estimated Parameter Accuracy

#### 4.4. Operating Conditions

## 5. Conclusions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Battery management system (BMS) functional features for battery electric vehicle lithium-ion batteries.

**Figure 3.**The relationship of the open circuit voltage with the state-of-charge. The OCV of a Lithium cobalt oxide (LCO) battery produced by Melasta Battery (Model No. SLPBB042126HN) with a capacity of 6550 mAh. The battery was cycled in an Arbin Instruments cycler at 25 °C. The OCV was estimated from cycling at a c-rate of c/20, and the SoC was estimated using the coulomb counting method.

**Figure 4.**The Kalman filter family of algorithms that have been used for state-of-charge estimation in battery electric vehicle Lithium-ion batteries.

**Figure 5.**Architecture of a generalized feedforward neural network of voltage (V), current (I), and time (T) inputs, a double layer and nodes where W is the weights, and the state-of-charge (SoC) output.

**Figure 6.**Sources of errors in model-based approaches to state-of-charge estimation in battery electric vehicle Lithium-ion batteries.

**Figure 7.**The decreasing voltage of two common LIB chemistries during discharge. The battery data were obtained from in [174] using low C-rate discharge (C/22), allowing the terminal voltage to be used to approximate the OCV.

Method | Maximum Error $(\le \pm )$ | |
---|---|---|

Look-up tables | OCV | 1.2% [58] |

Impedance | 1.4% [66] | |

Ampere-hour integral | Current integration | 4% [69] |

Filter | Linear Kalman | 2% [72] |

Extended Kalman | 1.4% [74] | |

Adaptive Kalman | 2% [80] | |

Sigma-point Kalman | 1.2% [85] | |

Unscented Kalman | 0.12% [87] | |

Adaptive unscented Kalman | 0.1% [94] | |

Central difference Kalman | 1.4% [98] | |

Cubature Kalman | 2.7% [101] | |

Particle | 0.86% [106] | |

Unscented particle | 0.9% [114] | |

Cubature particle | 1.1% [114] | |

Observer | Luenberger | 0.88% [118] |

Sliding mode | 2% [120] | |

Proportional integral | 2.5% [126] | |

H-infinity | 3.36% [128] | |

Data-driven | Genetic algorithm | 2.98% [33] |

Support vector machine | 6% [134] | |

Neural network | 3.8% [137] |

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**MDPI and ACS Style**

Espedal, I.B.; Jinasena, A.; Burheim, O.S.; Lamb, J.J. Current Trends for State-of-Charge (SoC) Estimation in Lithium-Ion Battery Electric Vehicles. *Energies* **2021**, *14*, 3284.
https://doi.org/10.3390/en14113284

**AMA Style**

Espedal IB, Jinasena A, Burheim OS, Lamb JJ. Current Trends for State-of-Charge (SoC) Estimation in Lithium-Ion Battery Electric Vehicles. *Energies*. 2021; 14(11):3284.
https://doi.org/10.3390/en14113284

**Chicago/Turabian Style**

Espedal, Ingvild B., Asanthi Jinasena, Odne S. Burheim, and Jacob J. Lamb. 2021. "Current Trends for State-of-Charge (SoC) Estimation in Lithium-Ion Battery Electric Vehicles" *Energies* 14, no. 11: 3284.
https://doi.org/10.3390/en14113284